Teaching Children Who Struggle with Mathematics : A Systematic Approach to Analysis and Correction

by Sherman, Helene J.; Richardson, Lloyd I.; Yard, George J.

• ISBN13: 9780130984630
• ISBN10: 0130984639
• Edition: 1st
• Format: Paperback
• Copyright: 2005-01-01
• Publisher: Prentice Hall

Summary

Until now, no book has dedicated itself more fully to addressing the cognitive needs of children in grades 1 through 6 who underachieve in mathematics. Teaching Children Who Struggle with Mathematics: A Systematic Approach to Analysis and Correction is designed to help teachers assess these students' individual abilities and characteristics as well as choose appropriate and effective instructional strategies. The book is rich with case studies of underachieving math students and assorted examples of how teachers can assess and differentiate instruction for these students through the use of two key text features-the Data Analysis Sheet (DAs) and the Math Improvement Plan (MIP). The DAS is used to record observed student behavior in a variety of relevant categories and to use such recordings to assess the student's math skills. The. MIP then provides an individualized plan for intervention and instruction upon completion of the DAs. When used together, the .DAS and MIP give teachers two powerful tools for properly assessing and teaching students who struggle with mathematics.

Table of Contents

The Dissimilar Learner and Mathematics Instruction	1	(16)
A Problem and a Solution	1	(1)
The Learner-Centered Approach	2	(1)
Systematic Instruction	2	(1)
Why Do Students Struggle with Mathematics?	2	(2)
Environmental Factors	3	(1)
Personal or Individualized Factors	3	(1)
How Is Mathematics Taught Effectively for All Students?	4	(10)
Developing Mathematics Proficiency	4	(3)
Valuing Mathematics	7	(1)
Meeting Standards for Dissimilar Learners	7	(2)
Identifying and Meeting the Needs of Dissimilar Learners	9	(5)
Conclusions	14	(1)
Discussion Questions	15	(1)
Bibliography	15	(2)
Place Value	17	(24)
The Impact of Place Value on Mathematics	17	(2)
What Is Place Value?	18	(1)
Why Do Students Struggle with Place Value?	19	(2)
Common Errors	19	(1)
Conceptual and Procedural Errors	19	(1)
About the Student: Colin	20	(1)
Error Patterns: Diagnosis, Prescription, Remediation	21	(15)
Place Value Error Pattern I for Colin	21	(7)
Place Value Error Pattern II for Colin	28	(4)
Place Value Error Pattern III for Colin	32	(4)
Conclusions: Instructional Strategies Summary	36	(2)
Instructional Activities	38	(2)
Discussion Questions	40	(1)
Bibliography	40	(1)
Addition of Whole Numbers	41	(24)
What Is Addition?	41	(2)
What Should Students Understand About Addition?	43	(1)
About the Student: Ian	43	(1)
Error Patterns: Diagnosis, Prescription, Remediation	44	(12)
Addition Error Pattern I for Ian	44	(6)
Addition Error Pattern II for Ian	50	(2)
Addition Error Pattern III for Ian	52	(4)
Conclusions: Instructional Strategies Summary	56	(1)
Instructional Activities	57	(3)
Discussion Questions	60	(2)
Bibliography	62	(3)
Subtraction of Whole Numbers	65	(24)
What Is Subtraction?	65	(2)
What Should Students Understand About Subtraction?	67	(1)
About the Student: Ernestine	67	(1)
Error Patterns: Diagnosis, Prescription, Remediation	68	(13)
Subtraction Error Pattern I for Ernestine	68	(5)
Subtraction Error Pattern II for Ernestine	73	(3)
Subtraction Error Pattern III for Ernestine	76	(5)
Conclusions: Instructional Strategies Summary	81	(1)
Instructional Activities	82	(2)
Discussion Questions	84	(2)
Bibliography	86	(3)
Multiplication	89	(24)
What Is Multiplication?	89	(1)
What Should Students Understand About Multiplication?	90	(1)
About the Student: Alberto	91	(1)
Error Patterns: Diagnosis, Prescription, Remediation	91	(13)
Multiplication Error Pattern I for Alberto	92	(5)
Multiplication Error Pattern II for Alberto	97	(4)
Multiplication Error Pattern III for Alberto	101	(3)
Conclusions: Instructional Strategies Summary	104	(1)
Instructional Activities	105	(5)
Discussion Questions	110	(2)
Bibliography	112	(1)
Division	113	(24)
What Is Division?	113	(1)
What Should Students Understand About Division?	114	(1)
About the Student: Marie	115	(1)
Error Patterns: Diagnosis, Prescription, Remediation	116	(14)
Division Error Pattern I for Marie	116	(6)
Division Error Pattern II for Marie	122	(6)
Division Error Pattern III for Marie	128	(2)
Conclusions: Instructional Strategies Summary	130	(2)
Instructional Activities	132	(1)
Discussion Questions	133	(2)
Bibliography	135	(2)
Rational Numbers	137	(38)
What Are Rational Numbers?	138	(1)
Why Do Students Struggle with Rational Numbers?	139	(1)
About the Student: Tawana	139	(1)
Error Patterns: Diagnosis, Prescription, Remediation	140	(26)
Rational Number Error Pattern I for Tawana	140	(8)
Rational Number Error Pattern II for Tawana	148	(5)
Rational Number Error Pattern III for Tawana	153	(4)
Rational Number Error Pattern IV for Tawana	157	(5)
Rational Number Error Pattern V for Tawana	162	(4)
Conclusions: Instructional Strategies Summary	166	(1)
Instructional Activities	167	(6)
Discussion Questions	173	(1)
Bibliography	173	(2)
Decimal Fractions	175	(30)
What Are Decimals?	175	(1)
Why Do Students Struggle with Decimals?	176	(1)
About the Student: Jose	177	(1)
Error Patterns: Diagnosis, Prescription, Remediation	177	(19)
Decimal Error Pattern I for Jose	177	(6)
Decimal Error Pattern II for Jose	183	(3)
Decimal Error Pattern III for Jose	186	(3)
Decimal Error Pattern IV for Jose	189	(3)
Decimal Error Pattern V for Jose	192	(4)
Conclusions: Instructional Strategies Summary	196	(1)
Instructional Activities	197	(6)
Discussion Questions	203	(1)
Bibliography	204	(1)
Problem Solving	205	(12)
What Is Problem Solving?	205	(2)
What Does Problem Solving Involve?	205	(2)
Types of Problems	207	(1)
Using Heuristics	207	(1)
Why Do Students Struggle with Solving Problems?	207	(2)
Literacy Issues	208	(1)
Number Sense Issues	208	(1)
Instructional Issues	209	(1)
Improving Students' Problem-Solving Ability	209	(2)
Instructional Strategies	209	(2)
Learning to Solve Problems	211	(3)
Problem Solving: Step by Step	211	(3)
Suggested Lesson Plan Structure	214	(1)
Conclusions: Instructional Strategies Summary	215	(1)
Discussion Questions	216	(1)
Bibliography	216	(1)
Appendix A Sample DAS and MIP Tables	217	(4)
Appendix B Suggestions for Planning Academic Content Lessons	221	(6)
Index	227

Excerpts

Me . . . math? That was always my worst subject. I stopped taking math as soon as I could. Is there much math required for this course/job/game/question? I'm just not a math person. I understood math until I got to algebra or geometry. I never really thought I needed math. My mother wasn't good at math, either. When asked about understanding and appreciating mathematics, people often reply that their comprehension is limited and their attitude is less than satisfactory. In fact, with little prompting, many individuals readily confess that they "never understood math," never "saw the use of it," and "got by" by taking the minimum number of courses to graduate from high school or college. Students such as those described above are termeddissimilar learnersin this book. They are not necessarily identified as having special needs and they may or may not have been provided extra resources despite making unsatisfactory progress. These pupils require well-designed alternative approaches to being taught and learning mathematics. The purpose of this book is to address the mathematics teaching and learning of underachieving students. They do not understand mathematical concepts sufficiently and/or are not as skillful as they could or would like to be in terms of executing math rules and symbolic computations. The authors believe that satisfactory achievement can be attained by adapting instruction to address influential classroom learning factors that affect dissimilar learners. Lessons and remediation must be designed in terms of developmental instructional strategies that promote thoughtful, active learning and connections to earlier concepts. Recognizing how learners adapt to learning environments and classroom organization in terms of preferences for reinforcement and methods for completing work are also critical learning factors. When teachers and parents focus on how their students learn best, rather than repeatedly offering the same or very similar instructional methods and materials, progress can be made. Students can move from believing they "can't do mathematics" to real achievement and confidence because instruction is targeted and effective. Features of this Text Unique to this book is a systemic approach designed to deal with variables that contribute to mathematics success. The authors created a Data Analysis Sheet (DAS), a template for considering learning characteristics and variables. These include the physical environment; the curriculum and current course of study; methods, strategies, and tools that students prefer for accepting and expressing information; academic behaviors; and responses from the environment that cause inappropriate or appropriate behavior to recur. After considering the learner's strengths and areas of concern, including the content to be taught, teachers complete a Mathematics Improvement Plan (MIP). With a student's academic and behavioral characteristics in mind, specific instructional approaches are planned to fit the daily schedule. Because these approaches are appropriate to those identified factors that best promote individual student learning, mathematics content improvement can occur. The approach to students' error patterns is another unique feature of this book. Each chapter deals with a different mathematics topic--from place value to problem solving--including whole numbers, fractions and decimals. A variety of errors made by typical students are described in a case study format. The reader can therefore examine patterns in terms of each child's learning and environmental characteristics. For example, Jose makes a number of decimal fraction errors described in the decimal /fractions chapter. Remediation strategies for addressing his misunderstandings are described in specific detail and in the context of the mathematical content and his case study, which highlights his academic an